1. Field of the Invention
The present invention relates to a general surface reconstruction system for bias field correction in MR images and more particularly to a shape-from-orientation system in a regularization framework to correct intensity inhomogenities in MR images.
2. Description of the Prior Art
Spatial intensity inhomogeneity induced by the radio frequency (RF) coil in magnetic resonance imaging (MRI) is a major problem in the computer analysis of MRI data. For example, the spatial intensity inhomogeneity has made the classification task in MRI very difficult for most of the existing segmentation methods. This is described by B. H. Brinkmann, A. Manduca and R. A. Robb, in "Quantitative Analysis Of Statistical Methods Of Grayscale Inhomogeneity Correction In Magnetic Resonance Images", Proc. SPIE Symposium On Medical Imaging: Image Processing, Vol. 2710, pp542-552, 1996, and by B. Johnston, M. S. Atkins, B. Mackiewich and M. Anderson, in "Segmentation Of Multiple Sclerosis Lesions In Intensity Corrected Multispectral MRI", IEEE Trans. Medical Imaging, Vol. 15, No. 2, pp. 154-169, 1996. This is due to the fact that the intensity inhomogeneities appearing in MR images produce spatial changes in tissue statistics, i.e. mean and variance. In addition, the degradation on the images obstructs the physician's diagnoses because the physician has to ignore the inhomogeneity artifact in the corrupted images. The spatial inhomogeneity is particularly severe in MR images acquired using surface coils. Therefore, the correction of spatial intensity inhomogeneity is regarded as an essential post-processing step to the computer analysis or processing of MRI.
The removal of the spatial intensity inhomogeneity from MR images is difficult since the inhomogeneities could change with different MRI acquisition parameters, from patients to patients and from slices to slices. Therefore, the correction of intensity inhomogeneities is usually required for each new image. A number of computer algorithms have been proposed for the intensity inhomogeneity correction in the last decade. B. R. Condon, J. Patterson, D. Wyper, A. Jenkins and D. M. Hadley, in "Image Non-uniformity In Magnetic Resonance Imaging: Its Magnitude And Methods For Correction", Brit. J. Radiol., Vol. 60, pp. 83-87, 1987, completed a thorough study of the magnitudes and types of grayscale nonuniformity. They also proposed two correction methods based on the signal produced by a uniform phantom. D. A. G. Wicks, G. J. Barker and P. S. Tofts, in "Correction Of Intensity Nonuniformity In MR Images Of Any Orientation", Magnetic Resonance Imaging, Vol. 11, pp. 183-196, 1993, followed the same approach and extended it to the correction for MR images of any orientation. Similarly, M. Tincher, C. R. Meyer, R. Gupta and D. M. Williams, in "Polynomial Modeling And Reduction Of RF Body Coil Spatial Inhomogeneity in MRI", IEEE Trans. Medical Imaging, Vol. 12, No. 2, pp. 361-365, 1993, modeled the inhomogeneity function by a second-order polynomial and fitted it to a uniform phantom scanned MR image. However, this phantom approach requires the same acquisition parameters for the phantom scan and the patient's. In addition, this approach assumes the intensity corruption effects are the same for different patients, which is not valid in general.
The homomorphic filtering approach described by B. Johnston, M. S. Atkins, B. Mackiewich and M. Anderson, in "Segmentation Of Multiple Sclerosis Lesions In Intensity Corrected Multispectral MRI", IEEE Trans. Medical Imaging, Vol. 15, No. 2, pp. 154-169, 1996, and by R. C. Gonzalez and R. E. Woods, in Digital Image Processing, Reading, M. A.: Addison-Wesley, 1993, has been commonly used due to its easy and efficient implementation. This approach is based on the assumption that the inhomogeneity function and the original uncorrupted signal are well separated in the frequency domain. Unfortunately, no justification of the above assumption has been made. Some researchers such as M. Tincher, C. R. Meyer, R. Gupta and D. M. Williams, in "Polynomial Modeling And Reduction Of RF Body Coil Spatial Inhomogeneity in MRI", IEEE Trans. Medical Imaging, Vol. 12, No. 2, pp. 361-365, 1993, and B. M. Dawant, A. P. Zijdenbos and R. A. Margolin, in "Correction Of Intensity Variations In MR Images For Computer-aided Tissue Classification", IEEE Trans. Medical Imaging, Vol. 12, No. 4, pp. 770-781, 1993, reported undesirable artifacts by using this approach.
B. M. Dawant, A. P. Zijdenbos and R. A. Margolin, in "Correction Of Intensity Variations In MR Images For Computer-aided Tissue Classification", IEEE Trans. Medical Imaging, Vol. 12, No. 4, pp. 770-781, 1993, proposed a surface fitting method to estimate the bias field. This method consists of selecting reference points in the same tissue class and fitting a thin-plate spline surface to these selected points. The reference points are selected either manually or through a tissue classification algorithm. The performance of this method substantially depends on the labeling of the reference points. Considerable user interactions are usually required to obtain good correction results. C. R. Meyer, P. H. Bland and J. Pipe in "Retrospective Correction Of Intensity Inhomogeneities In MRI", IEEE Trans. Medical Imaging, Vol. 14, No. 1, pp. 36-41, 1995, presented a polynomial fitting algorithm based on a prior segmentation of the corrupted MR image by using the Liou-Chiu-Jain segmentation algorithm. Note that the output of the segmentation is very critical to the correction result in this algorithm. As mentioned above, it is a very difficult task to obtain satisfactory segmentation results on the bias-field corrupted images. More recently, S. Gilles, M. Brady, J. Declerck, J. -P. Thirion and N. Ayache, in "Bias Field Correction Of Breast MR Images", Proceedings of the Fourth International Conference on Visualization in Biomedical Computing, pp. 153-158, Hamburg, Germany, Sep. 1996, proposed an automatic and iterative B-spline fitting algorithm for the intensity inhomogeneity correction of breast MR images. The application of this algorithm is restricted to the MR images with a single dominant tissue class, such as the breast MR images. Another polynomial surface fitting method described by C. Brechbuhler, G. Gerig and G. Szekely in "Compensation Of Spatial Inhomogeneity In MRI Based On A Parametric Bias Estimate", Proceedings of the Fourth International Conference on Visualization in Biomedical Computing, pp. 141-146, Hamburg, Germany, Sep. 1996, was proposed based on the assumption that the number of tissue classes, the true means and standard deviations of all the tissue classes in the image are given. Unfortunately, the required statistical information is usually not available.
As can be observed from previous works, the intensity inhomogeneity correction problem is strongly coupled with the segmentation problem. A primary goal for the inhomogeneity correction is to achieve better segmentation results, but many previous methods mentioned above require some classification information for the estimation of the bias field. Recently, W. M. Wells, III, W. E. L. Grimson, R. Kikinis and F. A. Jolesz in "Adaptive Segmentation Of MRI Data", IEEE Trans. Medical Imaging, Vol. 15, No. 4, pp. 429-442, 1996, developed a new statistical approach based on the EM algorithm to iteratively solve the bias field correction problem and the tissue classification problem altogether in an alternative fashion. R. Guillemaud and M. Brady in "Estimating The Bias Field Of MR Images", IEEE Trans. Medical Imaging, Vol. 16, No. 3, pp. 238-251, 1997, further refined this approach by introducing an extra class "other". In addition, they also explore the possibility of using the minimum entropy to automatically choose the number of tissue classes and the associated parameters. This is due to the fact that the performance of this statistical estimation approach is very sensitive to the number of classes that was provided by the user. There are two main disadvantages of this EM approach. At first, the computation involved in the EM algorithm is extremely intensive, especially for large problems. Secondly, the EM algorithm requires a good initial guess for either the bias field or the classification estimate. Otherwise, the EM algorithm could be easily trapped in a local minimum, resulting in an unsatisfactory solution.